arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1710.04073cs.SIcs.DMcs.DSphysics.data-anstat.ML
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流图和链接流用于随时间的交互建模

Stream Graphs and Link Streams for the Modeling of Interactions over Time

Matthieu Latapy, Tiphaine Viard, Clémence Magnien

摘要:

图论提供了一种研究关系结构的语言,它也经常被用来研究随着时间的推移的相互作用。然而,它很难捕捉到相互作用的时间和结构性质,这需要一个专门的形式主义。在本文中,我们推广图的概念,以应付这两个方面的一致的方式。我们从密度、聚类或路径等基本概念开始,并从中推导出更高级的概念,如团、度、聚类系数或连通分量。我们获得了一种语言来直接处理随着时间的推移的相互作用,类似于图形提供的语言来处理关系。这种形式主义是自洽的:不同概念之间的通常关系被保留。它也与图论一致:图概念是我们介绍的那些的特殊情况。这使得更高级别的对象,如商图,线图,k核和中心性的泛化变得容易。本文还考虑了离散与连续时间的假设,瞬时链接,并扩展到更复杂的情况下。

英文摘要:

Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a dedicated formalism. In this paper, we generalize graph concepts in order to cope with both aspects in a consistent way. We start with elementary concepts like density, clusters, or paths, and derive from them more advanced concepts like cliques, degrees, clustering coefficients, or connected components. We obtain a language to directly deal with interactions over time, similar to the language provided by graphs to deal with relations. This formalism is self-consistent: usual relations between different concepts are preserved. It is also consistent with graph theory: graph concepts are special cases of the ones we introduce. This makes it easy to generalize higher-level objects such as quotient graphs, line graphs, k-cores, and centralities. This paper also considers discrete versus continuous time assumptions, instantaneous links, and extensions to more complex cases.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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